Uses of Deep Learning
import numpy as np
import pandas as pd
import tensorflow as tf
from tensorflow import keras
print(tf.__version__)
2.9.2
# Simplest sequential layer neural network
model= tf.keras.Sequential([keras.layers.Dense(units=1, input_shape=[1])])
model.compile(optimizer='sgd', loss= 'mean_squared_error')
# numpy array for data
xs= np.array([-1.0, 0.0, 1.0, 2.0, 3.0, 4.0], dtype= float)
ys= np.array([-3.0, -1.0, 1.0, 3.0, 5.0, 7.0], dtype=float)
# Training of neural network
model.fit(xs, ys, epochs=500)
Epoch 1/500 1/1 [==============================] - 1s 548ms/step - loss: 52.0427 Epoch 2/500 1/1 [==============================] - 0s 8ms/step - loss: 41.3465 Epoch 3/500 1/1 [==============================] - 0s 12ms/step - loss: 32.9230 Epoch 4/500 1/1 [==============================] - 0s 10ms/step - loss: 26.2877 Epoch 5/500 1/1 [==============================] - 0s 11ms/step - loss: 21.0594 Epoch 6/500 1/1 [==============================] - 0s 10ms/step - loss: 16.9383 Epoch 7/500 1/1 [==============================] - 0s 8ms/step - loss: 13.6884 Epoch 8/500 1/1 [==============================] - 0s 8ms/step - loss: 11.1242 Epoch 9/500 1/1 [==============================] - 0s 6ms/step - loss: 9.0994 Epoch 10/500 1/1 [==============================] - 0s 7ms/step - loss: 7.4993 Epoch 11/500 1/1 [==============================] - 0s 7ms/step - loss: 6.2334 Epoch 12/500 1/1 [==============================] - 0s 7ms/step - loss: 5.2307 Epoch 13/500 1/1 [==============================] - 0s 19ms/step - loss: 4.4350 Epoch 14/500 1/1 [==============================] - 0s 12ms/step - loss: 3.8025 Epoch 15/500 1/1 [==============================] - 0s 9ms/step - loss: 3.2984 Epoch 16/500 1/1 [==============================] - 0s 10ms/step - loss: 2.8955 Epoch 17/500 1/1 [==============================] - 0s 8ms/step - loss: 2.5723 Epoch 18/500 1/1 [==============================] - 0s 8ms/step - loss: 2.3121 Epoch 19/500 1/1 [==============================] - 0s 6ms/step - loss: 2.1014 Epoch 20/500 1/1 [==============================] - 0s 9ms/step - loss: 1.9298 Epoch 21/500 1/1 [==============================] - 0s 7ms/step - loss: 1.7891 Epoch 22/500 1/1 [==============================] - 0s 8ms/step - loss: 1.6729 Epoch 23/500 1/1 [==============================] - 0s 7ms/step - loss: 1.5760 Epoch 24/500 1/1 [==============================] - 0s 9ms/step - loss: 1.4944 Epoch 25/500 1/1 [==============================] - 0s 6ms/step - loss: 1.4250 Epoch 26/500 1/1 [==============================] - 0s 7ms/step - loss: 1.3653 Epoch 27/500 1/1 [==============================] - 0s 11ms/step - loss: 1.3133 Epoch 28/500 1/1 [==============================] - 0s 8ms/step - loss: 1.2675 Epoch 29/500 1/1 [==============================] - 0s 14ms/step - loss: 1.2266 Epoch 30/500 1/1 [==============================] - 0s 8ms/step - loss: 1.1898 Epoch 31/500 1/1 [==============================] - 0s 10ms/step - loss: 1.1561 Epoch 32/500 1/1 [==============================] - 0s 12ms/step - loss: 1.1252 Epoch 33/500 1/1 [==============================] - 0s 9ms/step - loss: 1.0964 Epoch 34/500 1/1 [==============================] - 0s 8ms/step - loss: 1.0694 Epoch 35/500 1/1 [==============================] - 0s 7ms/step - loss: 1.0439 Epoch 36/500 1/1 [==============================] - 0s 8ms/step - loss: 1.0197 Epoch 37/500 1/1 [==============================] - 0s 8ms/step - loss: 0.9966 Epoch 38/500 1/1 [==============================] - 0s 9ms/step - loss: 0.9744 Epoch 39/500 1/1 [==============================] - 0s 7ms/step - loss: 0.9530 Epoch 40/500 1/1 [==============================] - 0s 8ms/step - loss: 0.9324 Epoch 41/500 1/1 [==============================] - 0s 9ms/step - loss: 0.9124 Epoch 42/500 1/1 [==============================] - 0s 8ms/step - loss: 0.8930 Epoch 43/500 1/1 [==============================] - 0s 8ms/step - loss: 0.8742 Epoch 44/500 1/1 [==============================] - 0s 7ms/step - loss: 0.8558 Epoch 45/500 1/1 [==============================] - 0s 7ms/step - loss: 0.8379 Epoch 46/500 1/1 [==============================] - 0s 11ms/step - loss: 0.8204 Epoch 47/500 1/1 [==============================] - 0s 6ms/step - loss: 0.8034 Epoch 48/500 1/1 [==============================] - 0s 13ms/step - loss: 0.7867 Epoch 49/500 1/1 [==============================] - 0s 11ms/step - loss: 0.7704 Epoch 50/500 1/1 [==============================] - 0s 9ms/step - loss: 0.7545 Epoch 51/500 1/1 [==============================] - 0s 7ms/step - loss: 0.7389 Epoch 52/500 1/1 [==============================] - 0s 8ms/step - loss: 0.7237 Epoch 53/500 1/1 [==============================] - 0s 7ms/step - loss: 0.7088 Epoch 54/500 1/1 [==============================] - 0s 8ms/step - loss: 0.6942 Epoch 55/500 1/1 [==============================] - 0s 8ms/step - loss: 0.6799 Epoch 56/500 1/1 [==============================] - 0s 9ms/step - loss: 0.6659 Epoch 57/500 1/1 [==============================] - 0s 7ms/step - loss: 0.6522 Epoch 58/500 1/1 [==============================] - 0s 8ms/step - loss: 0.6388 Epoch 59/500 1/1 [==============================] - 0s 8ms/step - loss: 0.6257 Epoch 60/500 1/1 [==============================] - 0s 7ms/step - loss: 0.6128 Epoch 61/500 1/1 [==============================] - 0s 7ms/step - loss: 0.6002 Epoch 62/500 1/1 [==============================] - 0s 7ms/step - loss: 0.5879 Epoch 63/500 1/1 [==============================] - 0s 7ms/step - loss: 0.5758 Epoch 64/500 1/1 [==============================] - 0s 8ms/step - loss: 0.5640 Epoch 65/500 1/1 [==============================] - 0s 10ms/step - loss: 0.5524 Epoch 66/500 1/1 [==============================] - 0s 7ms/step - loss: 0.5410 Epoch 67/500 1/1 [==============================] - 0s 7ms/step - loss: 0.5299 Epoch 68/500 1/1 [==============================] - 0s 7ms/step - loss: 0.5190 Epoch 69/500 1/1 [==============================] - 0s 7ms/step - loss: 0.5084 Epoch 70/500 1/1 [==============================] - 0s 8ms/step - loss: 0.4979 Epoch 71/500 1/1 [==============================] - 0s 8ms/step - loss: 0.4877 Epoch 72/500 1/1 [==============================] - 0s 7ms/step - loss: 0.4777 Epoch 73/500 1/1 [==============================] - 0s 7ms/step - loss: 0.4679 Epoch 74/500 1/1 [==============================] - 0s 11ms/step - loss: 0.4583 Epoch 75/500 1/1 [==============================] - 0s 7ms/step - loss: 0.4489 Epoch 76/500 1/1 [==============================] - 0s 6ms/step - loss: 0.4396 Epoch 77/500 1/1 [==============================] - 0s 6ms/step - loss: 0.4306 Epoch 78/500 1/1 [==============================] - 0s 6ms/step - loss: 0.4218 Epoch 79/500 1/1 [==============================] - 0s 7ms/step - loss: 0.4131 Epoch 80/500 1/1 [==============================] - 0s 7ms/step - loss: 0.4046 Epoch 81/500 1/1 [==============================] - 0s 8ms/step - loss: 0.3963 Epoch 82/500 1/1 [==============================] - 0s 8ms/step - loss: 0.3882 Epoch 83/500 1/1 [==============================] - 0s 8ms/step - loss: 0.3802 Epoch 84/500 1/1 [==============================] - 0s 14ms/step - loss: 0.3724 Epoch 85/500 1/1 [==============================] - 0s 8ms/step - loss: 0.3647 Epoch 86/500 1/1 [==============================] - 0s 8ms/step - loss: 0.3572 Epoch 87/500 1/1 [==============================] - 0s 7ms/step - loss: 0.3499 Epoch 88/500 1/1 [==============================] - 0s 16ms/step - loss: 0.3427 Epoch 89/500 1/1 [==============================] - 0s 8ms/step - loss: 0.3357 Epoch 90/500 1/1 [==============================] - 0s 8ms/step - loss: 0.3288 Epoch 91/500 1/1 [==============================] - 0s 7ms/step - loss: 0.3220 Epoch 92/500 1/1 [==============================] - 0s 10ms/step - loss: 0.3154 Epoch 93/500 1/1 [==============================] - 0s 7ms/step - loss: 0.3089 Epoch 94/500 1/1 [==============================] - 0s 10ms/step - loss: 0.3026 Epoch 95/500 1/1 [==============================] - 0s 7ms/step - loss: 0.2964 Epoch 96/500 1/1 [==============================] - 0s 9ms/step - loss: 0.2903 Epoch 97/500 1/1 [==============================] - 0s 7ms/step - loss: 0.2843 Epoch 98/500 1/1 [==============================] - 0s 7ms/step - loss: 0.2785 Epoch 99/500 1/1 [==============================] - 0s 7ms/step - loss: 0.2728 Epoch 100/500 1/1 [==============================] - 0s 8ms/step - loss: 0.2672 Epoch 101/500 1/1 [==============================] - 0s 7ms/step - loss: 0.2617 Epoch 102/500 1/1 [==============================] - 0s 7ms/step - loss: 0.2563 Epoch 103/500 1/1 [==============================] - 0s 7ms/step - loss: 0.2510 Epoch 104/500 1/1 [==============================] - 0s 8ms/step - loss: 0.2459 Epoch 105/500 1/1 [==============================] - 0s 8ms/step - loss: 0.2408 Epoch 106/500 1/1 [==============================] - 0s 7ms/step - loss: 0.2359 Epoch 107/500 1/1 [==============================] - 0s 7ms/step - loss: 0.2310 Epoch 108/500 1/1 [==============================] - 0s 7ms/step - loss: 0.2263 Epoch 109/500 1/1 [==============================] - 0s 7ms/step - loss: 0.2216 Epoch 110/500 1/1 [==============================] - 0s 7ms/step - loss: 0.2171 Epoch 111/500 1/1 [==============================] - 0s 7ms/step - loss: 0.2126 Epoch 112/500 1/1 [==============================] - 0s 10ms/step - loss: 0.2083 Epoch 113/500 1/1 [==============================] - 0s 7ms/step - loss: 0.2040 Epoch 114/500 1/1 [==============================] - 0s 7ms/step - loss: 0.1998 Epoch 115/500 1/1 [==============================] - 0s 7ms/step - loss: 0.1957 Epoch 116/500 1/1 [==============================] - 0s 8ms/step - loss: 0.1917 Epoch 117/500 1/1 [==============================] - 0s 8ms/step - loss: 0.1877 Epoch 118/500 1/1 [==============================] - 0s 7ms/step - loss: 0.1839 Epoch 119/500 1/1 [==============================] - 0s 7ms/step - loss: 0.1801 Epoch 120/500 1/1 [==============================] - 0s 8ms/step - loss: 0.1764 Epoch 121/500 1/1 [==============================] - 0s 8ms/step - loss: 0.1728 Epoch 122/500 1/1 [==============================] - 0s 9ms/step - loss: 0.1692 Epoch 123/500 1/1 [==============================] - 0s 7ms/step - loss: 0.1657 Epoch 124/500 1/1 [==============================] - 0s 7ms/step - loss: 0.1623 Epoch 125/500 1/1 [==============================] - 0s 7ms/step - loss: 0.1590 Epoch 126/500 1/1 [==============================] - 0s 7ms/step - loss: 0.1557 Epoch 127/500 1/1 [==============================] - 0s 14ms/step - loss: 0.1525 Epoch 128/500 1/1 [==============================] - 0s 7ms/step - loss: 0.1494 Epoch 129/500 1/1 [==============================] - 0s 7ms/step - loss: 0.1463 Epoch 130/500 1/1 [==============================] - 0s 7ms/step - loss: 0.1433 Epoch 131/500 1/1 [==============================] - 0s 7ms/step - loss: 0.1404 Epoch 132/500 1/1 [==============================] - 0s 10ms/step - loss: 0.1375 Epoch 133/500 1/1 [==============================] - 0s 8ms/step - loss: 0.1347 Epoch 134/500 1/1 [==============================] - 0s 8ms/step - loss: 0.1319 Epoch 135/500 1/1 [==============================] - 0s 7ms/step - loss: 0.1292 Epoch 136/500 1/1 [==============================] - 0s 7ms/step - loss: 0.1266 Epoch 137/500 1/1 [==============================] - 0s 7ms/step - loss: 0.1240 Epoch 138/500 1/1 [==============================] - 0s 7ms/step - loss: 0.1214 Epoch 139/500 1/1 [==============================] - 0s 8ms/step - loss: 0.1189 Epoch 140/500 1/1 [==============================] - 0s 7ms/step - loss: 0.1165 Epoch 141/500 1/1 [==============================] - 0s 12ms/step - loss: 0.1141 Epoch 142/500 1/1 [==============================] - 0s 7ms/step - loss: 0.1117 Epoch 143/500 1/1 [==============================] - 0s 7ms/step - loss: 0.1094 Epoch 144/500 1/1 [==============================] - 0s 7ms/step - loss: 0.1072 Epoch 145/500 1/1 [==============================] - 0s 7ms/step - loss: 0.1050 Epoch 146/500 1/1 [==============================] - 0s 7ms/step - loss: 0.1028 Epoch 147/500 1/1 [==============================] - 0s 8ms/step - loss: 0.1007 Epoch 148/500 1/1 [==============================] - 0s 13ms/step - loss: 0.0987 Epoch 149/500 1/1 [==============================] - 0s 13ms/step - loss: 0.0966 Epoch 150/500 1/1 [==============================] - 0s 8ms/step - loss: 0.0946 Epoch 151/500 1/1 [==============================] - 0s 7ms/step - loss: 0.0927 Epoch 152/500 1/1 [==============================] - 0s 7ms/step - loss: 0.0908 Epoch 153/500 1/1 [==============================] - 0s 7ms/step - loss: 0.0889 Epoch 154/500 1/1 [==============================] - 0s 7ms/step - loss: 0.0871 Epoch 155/500 1/1 [==============================] - 0s 37ms/step - loss: 0.0853 Epoch 156/500 1/1 [==============================] - 0s 6ms/step - loss: 0.0836 Epoch 157/500 1/1 [==============================] - 0s 6ms/step - loss: 0.0818 Epoch 158/500 1/1 [==============================] - 0s 6ms/step - loss: 0.0802 Epoch 159/500 1/1 [==============================] - 0s 7ms/step - loss: 0.0785 Epoch 160/500 1/1 [==============================] - 0s 7ms/step - loss: 0.0769 Epoch 161/500 1/1 [==============================] - 0s 7ms/step - loss: 0.0753 Epoch 162/500 1/1 [==============================] - 0s 50ms/step - loss: 0.0738 Epoch 163/500 1/1 [==============================] - 0s 19ms/step - loss: 0.0723 Epoch 164/500 1/1 [==============================] - 0s 146ms/step - loss: 0.0708 Epoch 165/500 1/1 [==============================] - 0s 31ms/step - loss: 0.0693 Epoch 166/500 1/1 [==============================] - 0s 11ms/step - loss: 0.0679 Epoch 167/500 1/1 [==============================] - 0s 8ms/step - loss: 0.0665 Epoch 168/500 1/1 [==============================] - 0s 8ms/step - loss: 0.0651 Epoch 169/500 1/1 [==============================] - 0s 7ms/step - loss: 0.0638 Epoch 170/500 1/1 [==============================] - 0s 8ms/step - loss: 0.0625 Epoch 171/500 1/1 [==============================] - 0s 8ms/step - loss: 0.0612 Epoch 172/500 1/1 [==============================] - 0s 10ms/step - loss: 0.0599 Epoch 173/500 1/1 [==============================] - 0s 10ms/step - loss: 0.0587 Epoch 174/500 1/1 [==============================] - 0s 9ms/step - loss: 0.0575 Epoch 175/500 1/1 [==============================] - 0s 8ms/step - loss: 0.0563 Epoch 176/500 1/1 [==============================] - 0s 14ms/step - loss: 0.0552 Epoch 177/500 1/1 [==============================] - 0s 10ms/step - loss: 0.0540 Epoch 178/500 1/1 [==============================] - 0s 11ms/step - loss: 0.0529 Epoch 179/500 1/1 [==============================] - 0s 11ms/step - loss: 0.0518 Epoch 180/500 1/1 [==============================] - 0s 8ms/step - loss: 0.0508 Epoch 181/500 1/1 [==============================] - 0s 6ms/step - loss: 0.0497 Epoch 182/500 1/1 [==============================] - 0s 6ms/step - loss: 0.0487 Epoch 183/500 1/1 [==============================] - 0s 6ms/step - loss: 0.0477 Epoch 184/500 1/1 [==============================] - 0s 6ms/step - loss: 0.0467 Epoch 185/500 1/1 [==============================] - 0s 18ms/step - loss: 0.0458 Epoch 186/500 1/1 [==============================] - 0s 11ms/step - loss: 0.0448 Epoch 187/500 1/1 [==============================] - 0s 11ms/step - loss: 0.0439 Epoch 188/500 1/1 [==============================] - 0s 9ms/step - loss: 0.0430 Epoch 189/500 1/1 [==============================] - 0s 11ms/step - loss: 0.0421 Epoch 190/500 1/1 [==============================] - 0s 12ms/step - loss: 0.0413 Epoch 191/500 1/1 [==============================] - 0s 10ms/step - loss: 0.0404 Epoch 192/500 1/1 [==============================] - 0s 9ms/step - loss: 0.0396 Epoch 193/500 1/1 [==============================] - 0s 8ms/step - loss: 0.0388 Epoch 194/500 1/1 [==============================] - 0s 9ms/step - loss: 0.0380 Epoch 195/500 1/1 [==============================] - 0s 6ms/step - loss: 0.0372 Epoch 196/500 1/1 [==============================] - 0s 7ms/step - loss: 0.0364 Epoch 197/500 1/1 [==============================] - 0s 6ms/step - loss: 0.0357 Epoch 198/500 1/1 [==============================] - 0s 6ms/step - loss: 0.0349 Epoch 199/500 1/1 [==============================] - 0s 5ms/step - loss: 0.0342 Epoch 200/500 1/1 [==============================] - 0s 6ms/step - loss: 0.0335 Epoch 201/500 1/1 [==============================] - 0s 10ms/step - loss: 0.0328 Epoch 202/500 1/1 [==============================] - 0s 7ms/step - loss: 0.0322 Epoch 203/500 1/1 [==============================] - 0s 13ms/step - loss: 0.0315 Epoch 204/500 1/1 [==============================] - 0s 5ms/step - loss: 0.0309 Epoch 205/500 1/1 [==============================] - 0s 9ms/step - loss: 0.0302 Epoch 206/500 1/1 [==============================] - 0s 6ms/step - loss: 0.0296 Epoch 207/500 1/1 [==============================] - 0s 7ms/step - loss: 0.0290 Epoch 208/500 1/1 [==============================] - 0s 6ms/step - loss: 0.0284 Epoch 209/500 1/1 [==============================] - 0s 6ms/step - loss: 0.0278 Epoch 210/500 1/1 [==============================] - 0s 6ms/step - loss: 0.0272 Epoch 211/500 1/1 [==============================] - 0s 7ms/step - loss: 0.0267 Epoch 212/500 1/1 [==============================] - 0s 5ms/step - loss: 0.0261 Epoch 213/500 1/1 [==============================] - 0s 5ms/step - loss: 0.0256 Epoch 214/500 1/1 [==============================] - 0s 6ms/step - loss: 0.0251 Epoch 215/500 1/1 [==============================] - 0s 5ms/step - loss: 0.0246 Epoch 216/500 1/1 [==============================] - 0s 6ms/step - loss: 0.0241 Epoch 217/500 1/1 [==============================] - 0s 6ms/step - loss: 0.0236 Epoch 218/500 1/1 [==============================] - 0s 7ms/step - loss: 0.0231 Epoch 219/500 1/1 [==============================] - 0s 7ms/step - loss: 0.0226 Epoch 220/500 1/1 [==============================] - 0s 7ms/step - loss: 0.0221 Epoch 221/500 1/1 [==============================] - 0s 7ms/step - loss: 0.0217 Epoch 222/500 1/1 [==============================] - 0s 7ms/step - loss: 0.0212 Epoch 223/500 1/1 [==============================] - 0s 8ms/step - loss: 0.0208 Epoch 224/500 1/1 [==============================] - 0s 8ms/step - loss: 0.0204 Epoch 225/500 1/1 [==============================] - 0s 8ms/step - loss: 0.0200 Epoch 226/500 1/1 [==============================] - 0s 7ms/step - loss: 0.0195 Epoch 227/500 1/1 [==============================] - 0s 7ms/step - loss: 0.0191 Epoch 228/500 1/1 [==============================] - 0s 6ms/step - loss: 0.0188 Epoch 229/500 1/1 [==============================] - 0s 7ms/step - loss: 0.0184 Epoch 230/500 1/1 [==============================] - 0s 8ms/step - loss: 0.0180 Epoch 231/500 1/1 [==============================] - 0s 7ms/step - loss: 0.0176 Epoch 232/500 1/1 [==============================] - 0s 8ms/step - loss: 0.0173 Epoch 233/500 1/1 [==============================] - 0s 13ms/step - loss: 0.0169 Epoch 234/500 1/1 [==============================] - 0s 7ms/step - loss: 0.0166 Epoch 235/500 1/1 [==============================] - 0s 9ms/step - loss: 0.0162 Epoch 236/500 1/1 [==============================] - 0s 7ms/step - loss: 0.0159 Epoch 237/500 1/1 [==============================] - 0s 6ms/step - loss: 0.0156 Epoch 238/500 1/1 [==============================] - 0s 6ms/step - loss: 0.0152 Epoch 239/500 1/1 [==============================] - 0s 7ms/step - loss: 0.0149 Epoch 240/500 1/1 [==============================] - 0s 7ms/step - loss: 0.0146 Epoch 241/500 1/1 [==============================] - 0s 7ms/step - loss: 0.0143 Epoch 242/500 1/1 [==============================] - 0s 7ms/step - loss: 0.0140 Epoch 243/500 1/1 [==============================] - 0s 6ms/step - loss: 0.0137 Epoch 244/500 1/1 [==============================] - 0s 7ms/step - loss: 0.0135 Epoch 245/500 1/1 [==============================] - 0s 6ms/step - loss: 0.0132 Epoch 246/500 1/1 [==============================] - 0s 9ms/step - loss: 0.0129 Epoch 247/500 1/1 [==============================] - 0s 7ms/step - loss: 0.0126 Epoch 248/500 1/1 [==============================] - 0s 8ms/step - loss: 0.0124 Epoch 249/500 1/1 [==============================] - 0s 7ms/step - loss: 0.0121 Epoch 250/500 1/1 [==============================] - 0s 7ms/step - loss: 0.0119 Epoch 251/500 1/1 [==============================] - 0s 6ms/step - loss: 0.0116 Epoch 252/500 1/1 [==============================] - 0s 7ms/step - loss: 0.0114 Epoch 253/500 1/1 [==============================] - 0s 7ms/step - loss: 0.0112 Epoch 254/500 1/1 [==============================] - 0s 6ms/step - loss: 0.0109 Epoch 255/500 1/1 [==============================] - 0s 6ms/step - loss: 0.0107 Epoch 256/500 1/1 [==============================] - 0s 6ms/step - loss: 0.0105 Epoch 257/500 1/1 [==============================] - 0s 6ms/step - loss: 0.0103 Epoch 258/500 1/1 [==============================] - 0s 6ms/step - loss: 0.0101 Epoch 259/500 1/1 [==============================] - 0s 6ms/step - loss: 0.0099 Epoch 260/500 1/1 [==============================] - 0s 7ms/step - loss: 0.0097 Epoch 261/500 1/1 [==============================] - 0s 8ms/step - loss: 0.0095 Epoch 262/500 1/1 [==============================] - 0s 6ms/step - loss: 0.0093 Epoch 263/500 1/1 [==============================] - 0s 6ms/step - loss: 0.0091 Epoch 264/500 1/1 [==============================] - 0s 7ms/step - loss: 0.0089 Epoch 265/500 1/1 [==============================] - 0s 7ms/step - loss: 0.0087 Epoch 266/500 1/1 [==============================] - 0s 8ms/step - loss: 0.0085 Epoch 267/500 1/1 [==============================] - 0s 7ms/step - loss: 0.0083 Epoch 268/500 1/1 [==============================] - 0s 8ms/step - loss: 0.0082 Epoch 269/500 1/1 [==============================] - 0s 6ms/step - loss: 0.0080 Epoch 270/500 1/1 [==============================] - 0s 6ms/step - loss: 0.0078 Epoch 271/500 1/1 [==============================] - 0s 6ms/step - loss: 0.0077 Epoch 272/500 1/1 [==============================] - 0s 6ms/step - loss: 0.0075 Epoch 273/500 1/1 [==============================] - 0s 6ms/step - loss: 0.0074 Epoch 274/500 1/1 [==============================] - 0s 6ms/step - loss: 0.0072 Epoch 275/500 1/1 [==============================] - 0s 7ms/step - loss: 0.0071 Epoch 276/500 1/1 [==============================] - 0s 7ms/step - loss: 0.0069 Epoch 277/500 1/1 [==============================] - 0s 9ms/step - loss: 0.0068 Epoch 278/500 1/1 [==============================] - 0s 8ms/step - loss: 0.0066 Epoch 279/500 1/1 [==============================] - 0s 7ms/step - loss: 0.0065 Epoch 280/500 1/1 [==============================] - 0s 7ms/step - loss: 0.0064 Epoch 281/500 1/1 [==============================] - 0s 8ms/step - loss: 0.0062 Epoch 282/500 1/1 [==============================] - 0s 7ms/step - loss: 0.0061 Epoch 283/500 1/1 [==============================] - 0s 7ms/step - loss: 0.0060 Epoch 284/500 1/1 [==============================] - 0s 7ms/step - loss: 0.0059 Epoch 285/500 1/1 [==============================] - 0s 7ms/step - loss: 0.0057 Epoch 286/500 1/1 [==============================] - 0s 7ms/step - loss: 0.0056 Epoch 287/500 1/1 [==============================] - 0s 37ms/step - loss: 0.0055 Epoch 288/500 1/1 [==============================] - 0s 15ms/step - loss: 0.0054 Epoch 289/500 1/1 [==============================] - 0s 8ms/step - loss: 0.0053 Epoch 290/500 1/1 [==============================] - 0s 7ms/step - loss: 0.0052 Epoch 291/500 1/1 [==============================] - 0s 7ms/step - loss: 0.0051 Epoch 292/500 1/1 [==============================] - 0s 9ms/step - loss: 0.0050 Epoch 293/500 1/1 [==============================] - 0s 7ms/step - loss: 0.0049 Epoch 294/500 1/1 [==============================] - 0s 9ms/step - loss: 0.0048 Epoch 295/500 1/1 [==============================] - 0s 7ms/step - loss: 0.0047 Epoch 296/500 1/1 [==============================] - 0s 7ms/step - loss: 0.0046 Epoch 297/500 1/1 [==============================] - 0s 7ms/step - loss: 0.0045 Epoch 298/500 1/1 [==============================] - 0s 11ms/step - loss: 0.0044 Epoch 299/500 1/1 [==============================] - 0s 7ms/step - loss: 0.0043 Epoch 300/500 1/1 [==============================] - 0s 6ms/step - loss: 0.0042 Epoch 301/500 1/1 [==============================] - 0s 6ms/step - loss: 0.0041 Epoch 302/500 1/1 [==============================] - 0s 16ms/step - loss: 0.0040 Epoch 303/500 1/1 [==============================] - 0s 6ms/step - loss: 0.0040 Epoch 304/500 1/1 [==============================] - 0s 10ms/step - loss: 0.0039 Epoch 305/500 1/1 [==============================] - 0s 11ms/step - loss: 0.0038 Epoch 306/500 1/1 [==============================] - 0s 15ms/step - loss: 0.0037 Epoch 307/500 1/1 [==============================] - 0s 12ms/step - loss: 0.0036 Epoch 308/500 1/1 [==============================] - 0s 7ms/step - loss: 0.0036 Epoch 309/500 1/1 [==============================] - 0s 7ms/step - loss: 0.0035 Epoch 310/500 1/1 [==============================] - 0s 13ms/step - loss: 0.0034 Epoch 311/500 1/1 [==============================] - 0s 10ms/step - loss: 0.0033 Epoch 312/500 1/1 [==============================] - 0s 6ms/step - loss: 0.0033 Epoch 313/500 1/1 [==============================] - 0s 6ms/step - loss: 0.0032 Epoch 314/500 1/1 [==============================] - 0s 7ms/step - loss: 0.0031 Epoch 315/500 1/1 [==============================] - 0s 6ms/step - loss: 0.0031 Epoch 316/500 1/1 [==============================] - 0s 6ms/step - loss: 0.0030 Epoch 317/500 1/1 [==============================] - 0s 6ms/step - loss: 0.0030 Epoch 318/500 1/1 [==============================] - 0s 5ms/step - loss: 0.0029 Epoch 319/500 1/1 [==============================] - 0s 5ms/step - loss: 0.0028 Epoch 320/500 1/1 [==============================] - 0s 6ms/step - loss: 0.0028 Epoch 321/500 1/1 [==============================] - 0s 6ms/step - loss: 0.0027 Epoch 322/500 1/1 [==============================] - 0s 9ms/step - loss: 0.0027 Epoch 323/500 1/1 [==============================] - 0s 6ms/step - loss: 0.0026 Epoch 324/500 1/1 [==============================] - 0s 59ms/step - loss: 0.0026 Epoch 325/500 1/1 [==============================] - 0s 49ms/step - loss: 0.0025 Epoch 326/500 1/1 [==============================] - 0s 10ms/step - loss: 0.0025 Epoch 327/500 1/1 [==============================] - 0s 18ms/step - loss: 0.0024 Epoch 328/500 1/1 [==============================] - 0s 9ms/step - loss: 0.0024 Epoch 329/500 1/1 [==============================] - 0s 56ms/step - loss: 0.0023 Epoch 330/500 1/1 [==============================] - 0s 7ms/step - loss: 0.0023 Epoch 331/500 1/1 [==============================] - 0s 32ms/step - loss: 0.0022 Epoch 332/500 1/1 [==============================] - 0s 8ms/step - loss: 0.0022 Epoch 333/500 1/1 [==============================] - 0s 7ms/step - loss: 0.0021 Epoch 334/500 1/1 [==============================] - 0s 10ms/step - loss: 0.0021 Epoch 335/500 1/1 [==============================] - 0s 35ms/step - loss: 0.0020 Epoch 336/500 1/1 [==============================] - 0s 14ms/step - loss: 0.0020 Epoch 337/500 1/1 [==============================] - 0s 55ms/step - loss: 0.0020 Epoch 338/500 1/1 [==============================] - 0s 13ms/step - loss: 0.0019 Epoch 339/500 1/1 [==============================] - 0s 12ms/step - loss: 0.0019 Epoch 340/500 1/1 [==============================] - 0s 13ms/step - loss: 0.0018 Epoch 341/500 1/1 [==============================] - 0s 14ms/step - loss: 0.0018 Epoch 342/500 1/1 [==============================] - 0s 6ms/step - loss: 0.0018 Epoch 343/500 1/1 [==============================] - 0s 6ms/step - loss: 0.0017 Epoch 344/500 1/1 [==============================] - 0s 6ms/step - loss: 0.0017 Epoch 345/500 1/1 [==============================] - 0s 5ms/step - loss: 0.0017 Epoch 346/500 1/1 [==============================] - 0s 5ms/step - loss: 0.0016 Epoch 347/500 1/1 [==============================] - 0s 6ms/step - loss: 0.0016 Epoch 348/500 1/1 [==============================] - 0s 6ms/step - loss: 0.0016 Epoch 349/500 1/1 [==============================] - 0s 10ms/step - loss: 0.0015 Epoch 350/500 1/1 [==============================] - 0s 6ms/step - loss: 0.0015 Epoch 351/500 1/1 [==============================] - 0s 6ms/step - loss: 0.0015 Epoch 352/500 1/1 [==============================] - 0s 23ms/step - loss: 0.0014 Epoch 353/500 1/1 [==============================] - 0s 9ms/step - loss: 0.0014 Epoch 354/500 1/1 [==============================] - 0s 12ms/step - loss: 0.0014 Epoch 355/500 1/1 [==============================] - 0s 16ms/step - loss: 0.0013 Epoch 356/500 1/1 [==============================] - 0s 8ms/step - loss: 0.0013 Epoch 357/500 1/1 [==============================] - 0s 10ms/step - loss: 0.0013 Epoch 358/500 1/1 [==============================] - 0s 12ms/step - loss: 0.0013 Epoch 359/500 1/1 [==============================] - 0s 11ms/step - loss: 0.0012 Epoch 360/500 1/1 [==============================] - 0s 9ms/step - loss: 0.0012 Epoch 361/500 1/1 [==============================] - 0s 7ms/step - loss: 0.0012 Epoch 362/500 1/1 [==============================] - 0s 9ms/step - loss: 0.0012 Epoch 363/500 1/1 [==============================] - 0s 8ms/step - loss: 0.0011 Epoch 364/500 1/1 [==============================] - 0s 10ms/step - loss: 0.0011 Epoch 365/500 1/1 [==============================] - 0s 12ms/step - loss: 0.0011 Epoch 366/500 1/1 [==============================] - 0s 8ms/step - loss: 0.0011 Epoch 367/500 1/1 [==============================] - 0s 8ms/step - loss: 0.0010 Epoch 368/500 1/1 [==============================] - 0s 10ms/step - loss: 0.0010 Epoch 369/500 1/1 [==============================] - 0s 10ms/step - loss: 0.0010 Epoch 370/500 1/1 [==============================] - 0s 7ms/step - loss: 9.8425e-04 Epoch 371/500 1/1 [==============================] - 0s 8ms/step - loss: 9.6403e-04 Epoch 372/500 1/1 [==============================] - 0s 8ms/step - loss: 9.4423e-04 Epoch 373/500 1/1 [==============================] - 0s 10ms/step - loss: 9.2484e-04 Epoch 374/500 1/1 [==============================] - 0s 9ms/step - loss: 9.0584e-04 Epoch 375/500 1/1 [==============================] - 0s 8ms/step - loss: 8.8724e-04 Epoch 376/500 1/1 [==============================] - 0s 11ms/step - loss: 8.6901e-04 Epoch 377/500 1/1 [==============================] - 0s 8ms/step - loss: 8.5116e-04 Epoch 378/500 1/1 [==============================] - 0s 9ms/step - loss: 8.3368e-04 Epoch 379/500 1/1 [==============================] - 0s 9ms/step - loss: 8.1655e-04 Epoch 380/500 1/1 [==============================] - 0s 8ms/step - loss: 7.9978e-04 Epoch 381/500 1/1 [==============================] - 0s 10ms/step - loss: 7.8335e-04 Epoch 382/500 1/1 [==============================] - 0s 10ms/step - loss: 7.6727e-04 Epoch 383/500 1/1 [==============================] - 0s 10ms/step - loss: 7.5151e-04 Epoch 384/500 1/1 [==============================] - 0s 8ms/step - loss: 7.3607e-04 Epoch 385/500 1/1 [==============================] - 0s 9ms/step - loss: 7.2095e-04 Epoch 386/500 1/1 [==============================] - 0s 8ms/step - loss: 7.0614e-04 Epoch 387/500 1/1 [==============================] - 0s 8ms/step - loss: 6.9163e-04 Epoch 388/500 1/1 [==============================] - 0s 8ms/step - loss: 6.7743e-04 Epoch 389/500 1/1 [==============================] - 0s 8ms/step - loss: 6.6351e-04 Epoch 390/500 1/1 [==============================] - 0s 8ms/step - loss: 6.4989e-04 Epoch 391/500 1/1 [==============================] - 0s 9ms/step - loss: 6.3653e-04 Epoch 392/500 1/1 [==============================] - 0s 12ms/step - loss: 6.2346e-04 Epoch 393/500 1/1 [==============================] - 0s 10ms/step - loss: 6.1066e-04 Epoch 394/500 1/1 [==============================] - 0s 11ms/step - loss: 5.9811e-04 Epoch 395/500 1/1 [==============================] - 0s 7ms/step - loss: 5.8583e-04 Epoch 396/500 1/1 [==============================] - 0s 7ms/step - loss: 5.7379e-04 Epoch 397/500 1/1 [==============================] - 0s 8ms/step - loss: 5.6201e-04 Epoch 398/500 1/1 [==============================] - 0s 8ms/step - loss: 5.5046e-04 Epoch 399/500 1/1 [==============================] - 0s 8ms/step - loss: 5.3916e-04 Epoch 400/500 1/1 [==============================] - 0s 8ms/step - loss: 5.2808e-04 Epoch 401/500 1/1 [==============================] - 0s 14ms/step - loss: 5.1723e-04 Epoch 402/500 1/1 [==============================] - 0s 7ms/step - loss: 5.0661e-04 Epoch 403/500 1/1 [==============================] - 0s 7ms/step - loss: 4.9621e-04 Epoch 404/500 1/1 [==============================] - 0s 6ms/step - loss: 4.8601e-04 Epoch 405/500 1/1 [==============================] - 0s 7ms/step - loss: 4.7603e-04 Epoch 406/500 1/1 [==============================] - 0s 7ms/step - loss: 4.6625e-04 Epoch 407/500 1/1 [==============================] - 0s 6ms/step - loss: 4.5667e-04 Epoch 408/500 1/1 [==============================] - 0s 6ms/step - loss: 4.4729e-04 Epoch 409/500 1/1 [==============================] - 0s 7ms/step - loss: 4.3810e-04 Epoch 410/500 1/1 [==============================] - 0s 7ms/step - loss: 4.2911e-04 Epoch 411/500 1/1 [==============================] - 0s 8ms/step - loss: 4.2029e-04 Epoch 412/500 1/1 [==============================] - 0s 8ms/step - loss: 4.1166e-04 Epoch 413/500 1/1 [==============================] - 0s 7ms/step - loss: 4.0320e-04 Epoch 414/500 1/1 [==============================] - 0s 15ms/step - loss: 3.9492e-04 Epoch 415/500 1/1 [==============================] - 0s 8ms/step - loss: 3.8681e-04 Epoch 416/500 1/1 [==============================] - 0s 8ms/step - loss: 3.7887e-04 Epoch 417/500 1/1 [==============================] - 0s 7ms/step - loss: 3.7108e-04 Epoch 418/500 1/1 [==============================] - 0s 8ms/step - loss: 3.6346e-04 Epoch 419/500 1/1 [==============================] - 0s 8ms/step - loss: 3.5599e-04 Epoch 420/500 1/1 [==============================] - 0s 7ms/step - loss: 3.4868e-04 Epoch 421/500 1/1 [==============================] - 0s 9ms/step - loss: 3.4152e-04 Epoch 422/500 1/1 [==============================] - 0s 14ms/step - loss: 3.3450e-04 Epoch 423/500 1/1 [==============================] - 0s 9ms/step - loss: 3.2764e-04 Epoch 424/500 1/1 [==============================] - 0s 9ms/step - loss: 3.2091e-04 Epoch 425/500 1/1 [==============================] - 0s 8ms/step - loss: 3.1431e-04 Epoch 426/500 1/1 [==============================] - 0s 8ms/step - loss: 3.0786e-04 Epoch 427/500 1/1 [==============================] - 0s 8ms/step - loss: 3.0153e-04 Epoch 428/500 1/1 [==============================] - 0s 8ms/step - loss: 2.9534e-04 Epoch 429/500 1/1 [==============================] - 0s 7ms/step - loss: 2.8927e-04 Epoch 430/500 1/1 [==============================] - 0s 8ms/step - loss: 2.8333e-04 Epoch 431/500 1/1 [==============================] - 0s 17ms/step - loss: 2.7751e-04 Epoch 432/500 1/1 [==============================] - 0s 10ms/step - loss: 2.7181e-04 Epoch 433/500 1/1 [==============================] - 0s 11ms/step - loss: 2.6623e-04 Epoch 434/500 1/1 [==============================] - 0s 7ms/step - loss: 2.6076e-04 Epoch 435/500 1/1 [==============================] - 0s 100ms/step - loss: 2.5540e-04 Epoch 436/500 1/1 [==============================] - 0s 9ms/step - loss: 2.5016e-04 Epoch 437/500 1/1 [==============================] - 0s 9ms/step - loss: 2.4502e-04 Epoch 438/500 1/1 [==============================] - 0s 11ms/step - loss: 2.3998e-04 Epoch 439/500 1/1 [==============================] - 0s 9ms/step - loss: 2.3506e-04 Epoch 440/500 1/1 [==============================] - 0s 9ms/step - loss: 2.3023e-04 Epoch 441/500 1/1 [==============================] - 0s 10ms/step - loss: 2.2550e-04 Epoch 442/500 1/1 [==============================] - 0s 10ms/step - loss: 2.2087e-04 Epoch 443/500 1/1 [==============================] - 0s 9ms/step - loss: 2.1633e-04 Epoch 444/500 1/1 [==============================] - 0s 10ms/step - loss: 2.1189e-04 Epoch 445/500 1/1 [==============================] - 0s 10ms/step - loss: 2.0753e-04 Epoch 446/500 1/1 [==============================] - 0s 9ms/step - loss: 2.0327e-04 Epoch 447/500 1/1 [==============================] - 0s 9ms/step - loss: 1.9909e-04 Epoch 448/500 1/1 [==============================] - 0s 11ms/step - loss: 1.9501e-04 Epoch 449/500 1/1 [==============================] - 0s 9ms/step - loss: 1.9100e-04 Epoch 450/500 1/1 [==============================] - 0s 10ms/step - loss: 1.8708e-04 Epoch 451/500 1/1 [==============================] - 0s 9ms/step - loss: 1.8323e-04 Epoch 452/500 1/1 [==============================] - 0s 10ms/step - loss: 1.7947e-04 Epoch 453/500 1/1 [==============================] - 0s 8ms/step - loss: 1.7578e-04 Epoch 454/500 1/1 [==============================] - 0s 13ms/step - loss: 1.7217e-04 Epoch 455/500 1/1 [==============================] - 0s 11ms/step - loss: 1.6864e-04 Epoch 456/500 1/1 [==============================] - 0s 11ms/step - loss: 1.6517e-04 Epoch 457/500 1/1 [==============================] - 0s 11ms/step - loss: 1.6178e-04 Epoch 458/500 1/1 [==============================] - 0s 7ms/step - loss: 1.5846e-04 Epoch 459/500 1/1 [==============================] - 0s 6ms/step - loss: 1.5520e-04 Epoch 460/500 1/1 [==============================] - 0s 6ms/step - loss: 1.5201e-04 Epoch 461/500 1/1 [==============================] - 0s 6ms/step - loss: 1.4889e-04 Epoch 462/500 1/1 [==============================] - 0s 10ms/step - loss: 1.4583e-04 Epoch 463/500 1/1 [==============================] - 0s 32ms/step - loss: 1.4284e-04 Epoch 464/500 1/1 [==============================] - 0s 8ms/step - loss: 1.3990e-04 Epoch 465/500 1/1 [==============================] - 0s 9ms/step - loss: 1.3703e-04 Epoch 466/500 1/1 [==============================] - 0s 9ms/step - loss: 1.3421e-04 Epoch 467/500 1/1 [==============================] - 0s 8ms/step - loss: 1.3146e-04 Epoch 468/500 1/1 [==============================] - 0s 10ms/step - loss: 1.2876e-04 Epoch 469/500 1/1 [==============================] - 0s 8ms/step - loss: 1.2611e-04 Epoch 470/500 1/1 [==============================] - 0s 8ms/step - loss: 1.2352e-04 Epoch 471/500 1/1 [==============================] - 0s 8ms/step - loss: 1.2098e-04 Epoch 472/500 1/1 [==============================] - 0s 12ms/step - loss: 1.1850e-04 Epoch 473/500 1/1 [==============================] - 0s 7ms/step - loss: 1.1606e-04 Epoch 474/500 1/1 [==============================] - 0s 12ms/step - loss: 1.1368e-04 Epoch 475/500 1/1 [==============================] - 0s 9ms/step - loss: 1.1135e-04 Epoch 476/500 1/1 [==============================] - 0s 9ms/step - loss: 1.0906e-04 Epoch 477/500 1/1 [==============================] - 0s 9ms/step - loss: 1.0682e-04 Epoch 478/500 1/1 [==============================] - 0s 12ms/step - loss: 1.0463e-04 Epoch 479/500 1/1 [==============================] - 0s 9ms/step - loss: 1.0248e-04 Epoch 480/500 1/1 [==============================] - 0s 10ms/step - loss: 1.0037e-04 Epoch 481/500 1/1 [==============================] - 0s 7ms/step - loss: 9.8308e-05 Epoch 482/500 1/1 [==============================] - 0s 12ms/step - loss: 9.6288e-05 Epoch 483/500 1/1 [==============================] - 0s 9ms/step - loss: 9.4309e-05 Epoch 484/500 1/1 [==============================] - 0s 10ms/step - loss: 9.2373e-05 Epoch 485/500 1/1 [==============================] - 0s 14ms/step - loss: 9.0477e-05 Epoch 486/500 1/1 [==============================] - 0s 8ms/step - loss: 8.8617e-05 Epoch 487/500 1/1 [==============================] - 0s 9ms/step - loss: 8.6797e-05 Epoch 488/500 1/1 [==============================] - 0s 8ms/step - loss: 8.5014e-05 Epoch 489/500 1/1 [==============================] - 0s 9ms/step - loss: 8.3268e-05 Epoch 490/500 1/1 [==============================] - 0s 10ms/step - loss: 8.1557e-05 Epoch 491/500 1/1 [==============================] - 0s 9ms/step - loss: 7.9883e-05 Epoch 492/500 1/1 [==============================] - 0s 9ms/step - loss: 7.8241e-05 Epoch 493/500 1/1 [==============================] - 0s 10ms/step - loss: 7.6634e-05 Epoch 494/500 1/1 [==============================] - 0s 9ms/step - loss: 7.5060e-05 Epoch 495/500 1/1 [==============================] - 0s 8ms/step - loss: 7.3518e-05 Epoch 496/500 1/1 [==============================] - 0s 8ms/step - loss: 7.2009e-05 Epoch 497/500 1/1 [==============================] - 0s 12ms/step - loss: 7.0530e-05 Epoch 498/500 1/1 [==============================] - 0s 14ms/step - loss: 6.9081e-05 Epoch 499/500 1/1 [==============================] - 0s 8ms/step - loss: 6.7662e-05 Epoch 500/500 1/1 [==============================] - 0s 7ms/step - loss: 6.6273e-05
<keras.callbacks.History at 0x7fc0a37ba940>
print(model.predict([10]))
1/1 [==============================] - 0s 92ms/step [[18.976248]]
print(model.predict([10, 20, 30, 44, 45.5]))
1/1 [==============================] - 0s 78ms/step [[18.976248] [38.941826] [58.907402] [86.85921 ] [89.85404 ]]
fashion_mnist= tf.keras.datasets.fashion_mnist
(train_image, train_labels), (test_image, test_labels)= fashion_mnist.load_data()
Downloading data from https://storage.googleapis.com/tensorflow/tf-keras-datasets/train-labels-idx1-ubyte.gz 29515/29515 [==============================] - 0s 0us/step Downloading data from https://storage.googleapis.com/tensorflow/tf-keras-datasets/train-images-idx3-ubyte.gz 26421880/26421880 [==============================] - 0s 0us/step Downloading data from https://storage.googleapis.com/tensorflow/tf-keras-datasets/t10k-labels-idx1-ubyte.gz 5148/5148 [==============================] - 0s 0us/step Downloading data from https://storage.googleapis.com/tensorflow/tf-keras-datasets/t10k-images-idx3-ubyte.gz 4422102/4422102 [==============================] - 0s 0us/step
import numpy as np
import matplotlib.pyplot as plt
# We can put between 0 to 59999 here
index=0
# Set number of characters per row when printing
np.set_printoptions(linewidth= 320)
# Print the label and image
print(f'LABEL:{train_labels[index]}')
print(f'\nIMAGE PIXEL ARRAY:\n {train_image[index]}')
# Visualize the image
plt.imshow(train_image[index])
LABEL:9 IMAGE PIXEL ARRAY: [[ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0] [ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0] [ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0] [ 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 13 73 0 0 1 4 0 0 0 0 1 1 0] [ 0 0 0 0 0 0 0 0 0 0 0 0 3 0 36 136 127 62 54 0 0 0 1 3 4 0 0 3] [ 0 0 0 0 0 0 0 0 0 0 0 0 6 0 102 204 176 134 144 123 23 0 0 0 0 12 10 0] [ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 155 236 207 178 107 156 161 109 64 23 77 130 72 15] [ 0 0 0 0 0 0 0 0 0 0 0 1 0 69 207 223 218 216 216 163 127 121 122 146 141 88 172 66] [ 0 0 0 0 0 0 0 0 0 1 1 1 0 200 232 232 233 229 223 223 215 213 164 127 123 196 229 0] [ 0 0 0 0 0 0 0 0 0 0 0 0 0 183 225 216 223 228 235 227 224 222 224 221 223 245 173 0] [ 0 0 0 0 0 0 0 0 0 0 0 0 0 193 228 218 213 198 180 212 210 211 213 223 220 243 202 0] [ 0 0 0 0 0 0 0 0 0 1 3 0 12 219 220 212 218 192 169 227 208 218 224 212 226 197 209 52] [ 0 0 0 0 0 0 0 0 0 0 6 0 99 244 222 220 218 203 198 221 215 213 222 220 245 119 167 56] [ 0 0 0 0 0 0 0 0 0 4 0 0 55 236 228 230 228 240 232 213 218 223 234 217 217 209 92 0] [ 0 0 1 4 6 7 2 0 0 0 0 0 237 226 217 223 222 219 222 221 216 223 229 215 218 255 77 0] [ 0 3 0 0 0 0 0 0 0 62 145 204 228 207 213 221 218 208 211 218 224 223 219 215 224 244 159 0] [ 0 0 0 0 18 44 82 107 189 228 220 222 217 226 200 205 211 230 224 234 176 188 250 248 233 238 215 0] [ 0 57 187 208 224 221 224 208 204 214 208 209 200 159 245 193 206 223 255 255 221 234 221 211 220 232 246 0] [ 3 202 228 224 221 211 211 214 205 205 205 220 240 80 150 255 229 221 188 154 191 210 204 209 222 228 225 0] [ 98 233 198 210 222 229 229 234 249 220 194 215 217 241 65 73 106 117 168 219 221 215 217 223 223 224 229 29] [ 75 204 212 204 193 205 211 225 216 185 197 206 198 213 240 195 227 245 239 223 218 212 209 222 220 221 230 67] [ 48 203 183 194 213 197 185 190 194 192 202 214 219 221 220 236 225 216 199 206 186 181 177 172 181 205 206 115] [ 0 122 219 193 179 171 183 196 204 210 213 207 211 210 200 196 194 191 195 191 198 192 176 156 167 177 210 92] [ 0 0 74 189 212 191 175 172 175 181 185 188 189 188 193 198 204 209 210 210 211 188 188 194 192 216 170 0] [ 2 0 0 0 66 200 222 237 239 242 246 243 244 221 220 193 191 179 182 182 181 176 166 168 99 58 0 0] [ 0 0 0 0 0 0 0 40 61 44 72 41 35 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0] [ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0] [ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]]
<matplotlib.image.AxesImage at 0x7fc09d01b610>
import numpy as np
import matplotlib.pyplot as plt
# We can put between 0 to 59999 here
index=1
# Set number of characters per row when printing
np.set_printoptions(linewidth= 320)
# Print the label and image
print(f'LABEL:{train_labels[index]}')
print(f'\nIMAGE PIXEL ARRAY:\n {train_image[index]}')
# Visualize the image
plt.imshow(train_image[index])
LABEL:0 IMAGE PIXEL ARRAY: [[ 0 0 0 0 0 1 0 0 0 0 41 188 103 54 48 43 87 168 133 16 0 0 0 0 0 0 0 0] [ 0 0 0 1 0 0 0 49 136 219 216 228 236 255 255 255 255 217 215 254 231 160 45 0 0 0 0 0] [ 0 0 0 0 0 14 176 222 224 212 203 198 196 200 215 204 202 201 201 201 209 218 224 164 0 0 0 0] [ 0 0 0 0 0 188 219 200 198 202 198 199 199 201 196 198 198 200 200 200 200 201 200 225 41 0 0 0] [ 0 0 0 0 51 219 199 203 203 212 238 248 250 245 249 246 247 252 248 235 207 203 203 222 140 0 0 0] [ 0 0 0 0 116 226 206 204 207 204 101 75 47 73 48 50 45 51 63 113 222 202 206 220 224 0 0 0] [ 0 0 0 0 200 222 209 203 215 200 0 70 98 0 103 59 68 71 49 0 219 206 214 210 250 38 0 0] [ 0 0 0 0 247 218 212 210 215 214 0 254 243 139 255 174 251 255 205 0 215 217 214 208 220 95 0 0] [ 0 0 0 45 226 214 214 215 224 205 0 42 35 60 16 17 12 13 70 0 189 216 212 206 212 156 0 0] [ 0 0 0 164 235 214 211 220 216 201 52 71 89 94 83 78 70 76 92 87 206 207 222 213 219 208 0 0] [ 0 0 0 106 187 223 237 248 211 198 252 250 248 245 248 252 253 250 252 239 201 212 225 215 193 113 0 0] [ 0 0 0 0 0 17 54 159 222 193 208 192 197 200 200 200 200 201 203 195 210 165 0 0 0 0 0 0] [ 0 0 0 0 0 0 0 47 225 192 214 203 206 204 204 205 206 204 212 197 218 107 0 0 0 0 0 0] [ 0 0 0 0 1 6 0 46 212 195 212 202 206 205 204 205 206 204 212 200 218 91 0 3 1 0 0 0] [ 0 0 0 0 0 1 0 11 197 199 205 202 205 206 204 205 207 204 205 205 218 77 0 5 0 0 0 0] [ 0 0 0 0 0 3 0 2 191 198 201 205 206 205 205 206 209 206 199 209 219 74 0 5 0 0 0 0] [ 0 0 0 0 0 2 0 0 188 197 200 207 207 204 207 207 210 208 198 207 221 72 0 4 0 0 0 0] [ 0 0 0 0 0 2 0 0 215 198 203 206 208 205 207 207 210 208 200 202 222 75 0 4 0 0 0 0] [ 0 0 0 0 0 1 0 0 212 198 209 206 209 206 208 207 211 206 205 198 221 80 0 3 0 0 0 0] [ 0 0 0 0 0 1 0 0 204 201 205 208 207 205 211 205 210 210 209 195 221 96 0 3 0 0 0 0] [ 0 0 0 0 0 1 0 0 202 201 205 209 207 205 213 206 210 209 210 194 217 105 0 2 0 0 0 0] [ 0 0 0 0 0 1 0 0 204 204 205 208 207 205 215 207 210 208 211 193 213 115 0 2 0 0 0 0] [ 0 0 0 0 0 0 0 0 204 207 207 208 206 206 215 210 210 207 212 195 210 118 0 2 0 0 0 0] [ 0 0 0 0 0 1 0 0 198 208 208 208 204 207 212 212 210 207 211 196 207 121 0 1 0 0 0 0] [ 0 0 0 0 0 1 0 0 198 210 207 208 206 209 213 212 211 207 210 197 207 124 0 1 0 0 0 0] [ 0 0 0 0 0 0 0 0 172 210 203 201 199 204 207 205 204 201 205 197 206 127 0 0 0 0 0 0] [ 0 0 0 0 0 0 0 0 188 221 214 234 236 238 244 244 244 240 243 214 224 162 0 2 0 0 0 0] [ 0 0 0 0 0 1 0 0 139 146 130 135 135 137 125 124 125 121 119 114 130 76 0 0 0 0 0 0]]
<matplotlib.image.AxesImage at 0x7fc09cb56d00>
# Normalize the pixel values of the train and test images (0-1) range
training_images= train_image/255.0
test_image= test_image/255.0
model= keras.Sequential([
keras.layers.Flatten(),
keras.layers.Dense(128, activation= tf.nn.relu),
keras.layers.Dense(10, activation= tf.nn.softmax)
])
model= keras.Sequential([
keras.layers.Flatten(input_shape= (28, 28)),
keras.layers.Dense(128, activation= tf.nn.relu),
keras.layers.Dense(10, activation= tf.nn.softmax)
])
$\quad\,\,\,\,$ Flatten converts $28 \times 28$ into a simple linear layer.
# Declare teh sampel inputs and convert to a tensor
inputs= np.array([[1.0, 3.0, 4.0, 2.0]])
inputs= tf.convert_to_tensor(inputs)
print(f'input to softmax function: {inputs.numpy()}')
# Feed the inputs to a softmax activation function
outputs= tf.keras.activations.softmax(inputs)
print(f'output to softmax function: {outputs.numpy()}')
# Get teh sum of all values after the softmax
sum= tf.reduce_sum(outputs)
print(f'sum of outputs: {sum}')
# Get the index with highest value
prediction= np.argmax(outputs)
print(f'class with highest probability: {prediction}')
input to softmax function: [[1. 3. 4. 2.]] output to softmax function: [[0.0320586 0.23688282 0.64391426 0.08714432]] sum of outputs: 1.0 class with highest probability: 2
model.compile(optimizer= tf.optimizers.Adam(),
loss= 'sparse_categorical_crossentropy',
metrics= ['accuracy'])
model.fit(training_images, train_labels, epochs= 5)
Epoch 1/5 1875/1875 [==============================] - 6s 3ms/step - loss: 0.4961 - accuracy: 0.8264 Epoch 2/5 1875/1875 [==============================] - 6s 3ms/step - loss: 0.3776 - accuracy: 0.8652 Epoch 3/5 1875/1875 [==============================] - 6s 3ms/step - loss: 0.3375 - accuracy: 0.8767 Epoch 4/5 1875/1875 [==============================] - 6s 3ms/step - loss: 0.3115 - accuracy: 0.8863 Epoch 5/5 1875/1875 [==============================] - 6s 3ms/step - loss: 0.2940 - accuracy: 0.8921
<keras.callbacks.History at 0x7fc09cafde50>
# Evaluate the model on unseen data
model.evaluate(test_image, test_labels)
313/313 [==============================] - 2s 4ms/step - loss: 0.3752 - accuracy: 0.8611
[0.37521636486053467, 0.8611000180244446]
An Activation function is a critical part of the design of a neural network.
An activation function in a neural network defines how the weighted sum of the input is transformed into an output from a node or nodes in a layer of the network.
Sometimes the activation function is called a "transfer function".
If the output range of the activation function is limited then it may be called a "squashing function".
Many activations are nonlinear and may be referred to as the "nonlinearity" in the layer or the network design.
Tonnes of data is available
$$\text{Activation functions help us to deal with it.}$$ Activation functions are mathematical equations that determine the output of a neural network model. They help the network to use the important information and suppress the noise.
A simple model of neuron commonly known as the perception. It can be divided into three parts:
i. Input layer
ii. Neuron
iii. Output Layer
We first calculate the weighted sum of the input i.e. $$\sum_{i=1}^n w_i*x_i$$
Then Activation function is applied as. $$\phi\Bigg(\sum_{i=1}^n w_i*x_i\Bigg)$$
The calculate value is then passed to the next layer if present.
$$z= \sum_i w_ix_i+ b$$But:
The linear activation function, also known as "no activation" or "identify function" (multiplied $x_1.0$), is where the activation is proportional to the input
The function doesn't do anything to the weighted sum of the input, it simply spits out the value it was given as shown previously. $$f(x)= x$$
A linear activation function has two major problems :
The limited power linear activation function (simply a linear regression model), this does not allow the model to create complex mappings between the network's inputs and outputs.
Bianry step function is a threshold-based function which means:
In the graph, the threshold is zero. This activation can be used in binary classification as the name suggest, however it can not be used in a situation where you have multiple classes to deal with.
where $e$ is a mathematical constant, which is the base of the natural logarithm.
Why sigmoid function is most widely used:
This is represented by S-shape of the sigmoid activation function.
$$\text{However, Sigmoid function makes almost no change in the prediction for very high or very low inputs which ultimately results in neural network refusing to learn further, this problem is known as the vanishing gradient.}$$where $e$ is a mathematical constant, which is the base of the natural logarithm.
where $a$ is the slope parameter for negative values.
$$\text{ReLU} \quad\quad\quad \rightarrow \text{Leaky ReLU} \quad\quad\quad\quad\quad \rightarrow \text{Parametric ReLU}$$$$f(x)= max(0, x) \quad\quad \rightarrow f(x)= max(0.1x, x) \quad\quad \rightarrow f(x)= max(ax, x)$$The output of the sigmoid function was in the range of 0 to 1, which can be thought of as probability.
But ---
This function faces certain problems.
e.g.
Let'suppose we have five output values of $0.8, 0.9, 0.7, 0.8$ and $0.6$ respectively.
How we can move forward with it ?
The answer is: We can't.
The above values don't make sense as the sum of all teh classes/output probabilities should be equal to $1$.
Use sigmoid fuction in output layer, use tanh in all other places.
But both of these have vanishing gradient problem.
Leakly ReLU or Parametric ReLU can be used here then to reduce teh computation.
Most Widely used Activation functions for hidden layers:
Hyperbolic Tangent (Tanh)
ReLU is the most common activation function used for the hidden layers.
The activation function used in hidden layers is typically chosen based on the type of neural network architecture.
Most widely used activation functions for output layer:
The linear activation function is also called "identity" (multiplied by 1.0) or "no activation".
This is because the linear activation function does not change the weighted sum of the input in any way and instead returns the value directly.
How to choose the best activation function ?
If your problem is a regression problem, you should use a linear activation function.
If your problem is a classification problem, then there are three main types of classification problems and each may use a different activation function.